Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation
Provides theoretical and numerical tools for analyzing thin-film flows on rotating cylinders, relevant to fluid dynamics researchers.
The paper proves that steady-state solutions of a thin-film equation on a rotating cylinder are strictly positive for nonzero rotation speeds, and develops an iterative spectral algorithm for computing them.
We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate an iterative spectral algorithm for computing these steady states. Finally, we explore a non-existence inequality for steady state solutions from the recent work of Chugunova, Pugh, & Taranets.